{"doi":"10.1162/089976698300017467","title":"Nonlinear Component Analysis as a Kernel Eigenvalue Problem","abstract":"<jats:p> A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in high-dimensional feature spaces, related to input space by some nonlinear map—for instance, the space of all possible five-pixel products in 16 × 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition. </jats:p>","journal":"Neural Computation","year":1998,"id":6074,"datarank":23.264591614082693,"base_score":8.992930352509733,"endowment":8.992930352509733,"self_citation_contribution":1.34893955287646,"citation_network_contribution":21.915652061206234,"self_endowment_contribution":1.34893955287646,"citer_contribution":21.915652061206234,"corpus_percentile":95.0,"corpus_rank":1785,"citation_count":8045,"citer_count":177,"citers_with_citation_signal":177,"citers_with_endowment":177,"datacite_reuse_total":0,"is_dataset":false,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"1998-07-01","authors":[{"id":57411,"name":"Alexander Smola","orcid":null,"position":1,"is_corresponding":false},{"id":57412,"name":"Klaus-Robert Müller","orcid":"0000-0002-3861-7685","position":2,"is_corresponding":false},{"id":57413,"name":"Alexander J. Smola","orcid":"0000-0002-7963-4721","position":3,"is_corresponding":false},{"id":39729,"name":"Klaus‐Robert Müller","orcid":null,"position":4,"is_corresponding":false},{"id":2771,"name":"Bernhard Schölkopf","orcid":"0000-0002-8177-0925","position":0,"is_corresponding":true}],"reference_count":7,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}